15x^2-7x-6=0

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Solution for 15x^2-7x-6=0 equation: 


Simplifying
15x2 + -7x + -6 = 0

Reorder the terms:
-6 + -7x + 15x2 = 0

Solving
-6 + -7x + 15x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
15 the coefficient of the squared term: 

Divide each side by '15'.
-0.4 + -0.4666666667x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -0.4666666667x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -0.4666666667x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -0.4666666667x + x2 = 0 + 0.4
-0.4666666667x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-0.4666666667x + x2 = 0.4

The x term is -0.4666666667x.  Take half its coefficient (-0.2333333334).
Square it (0.05444444448) and add it to both sides.

Add '0.05444444448' to each side of the equation.
-0.4666666667x + 0.05444444448 + x2 = 0.4 + 0.05444444448

Reorder the terms:
0.05444444448 + -0.4666666667x + x2 = 0.4 + 0.05444444448

Combine like terms: 0.4 + 0.05444444448 = 0.45444444448
0.05444444448 + -0.4666666667x + x2 = 0.45444444448

Factor a perfect square on the left side:
(x + -0.2333333334)(x + -0.2333333334) = 0.45444444448

Calculate the square root of the right side: 0.674124947

Break this problem into two subproblems by setting 
(x + -0.2333333334) equal to 0.674124947 and -0.674124947.


Subproblem 1
x + -0.2333333334 = 0.674124947

Simplifying
x + -0.2333333334 = 0.674124947

Reorder the terms:
-0.2333333334 + x = 0.674124947

Solving
-0.2333333334 + x = 0.674124947

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.2333333334' to each side of the equation.
-0.2333333334 + 0.2333333334 + x = 0.674124947 + 0.2333333334

Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000
0.0000000000 + x = 0.674124947 + 0.2333333334
x = 0.674124947 + 0.2333333334

Combine like terms: 0.674124947 + 0.2333333334 = 0.9074582804
x = 0.9074582804

Simplifying
x = 0.9074582804


Subproblem 2
x + -0.2333333334 = -0.674124947

Simplifying
x + -0.2333333334 = -0.674124947

Reorder the terms:
-0.2333333334 + x = -0.674124947

Solving
-0.2333333334 + x = -0.674124947

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.2333333334' to each side of the equation.
-0.2333333334 + 0.2333333334 + x = -0.674124947 + 0.2333333334

Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000
0.0000000000 + x = -0.674124947 + 0.2333333334
x = -0.674124947 + 0.2333333334

Combine like terms: -0.674124947 + 0.2333333334 = -0.4407916136
x = -0.4407916136

Simplifying
x = -0.4407916136


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9074582804, -0.4407916136}

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